This problem gives a simple example of a quantitative structure– activity relation (QSAR). The binding of nonpolar groups of amino acid to hydrophobic sites in the interior of proteins is governed largely by hydrophobic interactions. 

(a) Consider a family of hydrocarbons ReH. The hydrophobicity constants, π, for RaCH₃, CH₂CH₃, (CH₂)₂CH₃, (CH₂)₃CH₃, and (CH₂)₄CH₃ are, respectively, 0.5, 1.0, 1.5, 2.0, and 2.5. Use these data to predict the π value for (CH₂)₆CH₃.

(b) The equilibrium constants K_I for the dissociation of inhibitors (9) from the enzyme chymotrypsin were measured for different substituents R:

Plot log KI against π. Does the plot suggest a linear relationship? If so, what are the slope and intercept to the log KI axis of the line that best fits the data?

(c) Predict the value of K_I for the case R=H.

R R log K CH,CO -0.20 -1.73 CN -0.025 -1.90 NO 0.33 -2.43 CH3 0.5 -2.55 0.9 -3.40